On 25 Dec 2008, at 22:27, Kim Jones wrote:
> > > On 26/12/2008, at 5:23 AM, Bruno Marchal wrote: > >> >> On 25 Dec 2008, at 08:05, Abram Demski wrote: >> >>> >>> Bruno, >>> >>> I agree with Gunther about the two types of machine. The broader >>> machine is any system that can be logically described-- a system >>> that >>> is governed by rules and has a definite description. >> >> Then Church thesis entails it is not broader, unless you mean that >> the rules are not effective. >> >> >> > > I might be missing something here, but somebody please give an example > of a system that is NOT governed by rules and possesses NO definite > description. Arithmetical truth. That is, the set of all true sentences of elementary arithmetic. The set of Gödel number, or description of never stopping programs or machines. The set of descriptions (in any universal language) of any non trivial machines. At the first order level: all the arithmetical hypostases. Sigma_2 truth, Sigma_3 truth, Sigma_4 truth, Sigma_5 truth, Sigma_6 truth, etc. (the union of which gives arithmetical truth) Analytical truth (far beyond arithmetical truth). Mathematical Truth (if that exists). Kim, all those exemples provide well defined set of objects, (except the last one) but there is no way to generate them by any machine, nor can we axiomatize them in any effective way. No effective complete "Theory" for any of them. Alas, there is a need of some math to prove this. If you are patient, when we get the seven step of UDA, I will have to give you at least a tool (diagonalization) capable of easily showing the existence and the non effectivity of those non mechanical mathematical realities. It is needed to be more precise on "effectivity" to discover the non- effectivity. Mechanism is not a reductionism, (as I explain often to John Mikes) because Universal machines behaviors depends on those non effective things. Creation and life appears on the border between the computable and the non computable. It is similar to the border of the Mandelbrot set. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
